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The level set method has been widely applied in topology optimization of mechanical structures, primarily for linear materials, but its application to nonlinear hyperelastic materials, particularly for compliant mechanisms, remains largely unexplored. This paper addresses this gap by developing a comprehensive level set-based topology optimization framework specifically for designing compliant mechanisms using neo-Hookean hyperelastic materials. A key advantage of hyperelastic materials is their ability to undergo large, reversible deformations, making them well-suited for soft robotics and biomedical applications. However, existing nonlinear topology optimization studies using the level set method mainly focus on stiffness optimization and often rely on linear results as preliminary approximations. Our framework rigorously derives the shape sensitivity analysis using the adjoint method, including crucial higher-order displacement gradient terms often neglected in simplified approaches. By retaining these terms, we achieve more accurate boundary evolution during optimization, leading to improved convergence behavior and more effective structural designs. The proposed approach is first validated with a mean compliance problem as a benchmark, demonstrating its ability to generate optimized structural configurations while addressing the nonlinear behavior of hyperelastic materials. Subsequently, we extend the method to design a displacement inverter compliant mechanism that fully exploits the advantages of hyperelastic materials in achieving controlled large deformations. The resulting designs feature smooth boundaries and clear structural features that effectively leverage the material's nonlinear properties. This work provides a robust foundation for designing advanced compliant mechanisms with large deformation capabilities, extending the reach of topology optimization into new application domains where traditional linear approaches are insufficient. The developed methodology is expected to provide a timely solution to computational design for soft robotics, flexible mechanisms, and other emerging technologies that benefit from hyperelastic material properties. 

Abstract Minimally invasive endovascular therapy (MIET) is an innovative technique that utilizes percutaneous access and transcatheter implantation of medical devices to treat vascular diseases. However, conventional devices often face limitations such as incomplete or suboptimal treatment, leading to issues like recanalization in brain aneurysms, endoleaks in aortic aneurysms, and paravalvular leaks in cardiac valves. In this study, we introduce a new metastructure design for MIET employing re-entrant honeycomb structures with negative Poisson’s ratio (NPR), which are initially designed through topology optimization and subsequently mapped onto a cylindrical surface. Using ferromagnetic soft materials, we developed structures with adjustable mechanical properties called magnetically activated structures (MAS). These magnetically activated structures can change shape under noninvasive magnetic fields, letting them fit against blood vessel walls to fix leaks or movement issues. The soft ferromagnetic materials allow the stent design to be remotely controlled, changed, and rearranged using external magnetic fields. This offers accurate control over stent placement and positioning inside blood vessels. We performed magneto-mechanical simulations to evaluate the proposed design’s performance. Experimental tests were conducted on prototype beams to assess their bending and torsional responses to external magnetic fields. The simulation results were compared with experimental data to determine the accuracy of the magneto-mechanical simulation model for ferromagnetic soft materials. After validating the model, it was used to analyze the deformation behavior of the plane matrix and cylindrical structure designs of the Negative Poisson’s Ratio (NPR) metamaterial. The results indicate that the plane matrix NPR metamaterial design exhibits concurrent vertical and horizontal expansion when subjected to an external magnetic field. In contrast, the cylindrical structure demonstrates simultaneous axial and radial expansion under the same conditions. The preliminary findings demonstrate the considerable potential and practicality of the proposed methodology in the development of magnetically activated MIET devices, which offer biocompatibility, a diminished risk of adverse reactions, and enhanced therapeutic outcomes. Integrating ferromagnetic soft materials into mechanical metastructures unlocks promising opportunities for designing stents with adjustable mechanical properties, propelling the field towards more sophisticated minimally invasive vascular interventions. 

Generators are considered as the core application of electromagnetic machines, which require high-cost rare-earth-based permanent magnets. The development of generators is moving toward high efficiency and increased environmental friendliness. Minimizing the use of rare earth materials such as magnetic materials under the premise of machine performance emerges as a challenging task. Topology optimization has been promisingly applied to many application areas as a powerful generative design tool. It can identify the optimal distribution of magnetic material in the defined design space. This paper employs the level-set-based topology optimization method to design the permanent magnet for generators. The machine under study is a simplified 2D outer rotor direct-drive wind power generator. The dynamic and static models of this generator are studied, and the magnetostatic system is adopted to conduct the topology optimization. The optimization goals in this study mainly focused on two aspects, namely the maximization of the system magnetic energy and the generation of a target magnetic field in the region of the air gap. The continuum shape sensitivity analysis is derived by using the material time derivative, the Lagrange multiplier method, and the adjoint variable method. Two numerical examples are investigated, and the effectiveness of the proposed design framework is validated by comparing the performance of the original design against the optimized design.